Ed Miliband is seeking a meeting with David Cameron and Nick Clegg this week to thrash out an agreement on how to implement the Leveson report on future press standards amid Labour fears that ministers are manoeuvring to delay a decision until the public interest ebbs away in the new year.

Labour had been expecting by lunchtime on Monday to receive the government’s version of a draft bill on future press self-regulation, as well as alternative proposals drawn up by Cameron’s policy fixer, Oliver Letwin, on how the press could be made subject to a royal charter.

Liberal Democrats for the first time briefed that they were not opposed to the idea of a royal charter in principle if it could be shown to work. They also argued progress had been relatively swift, and said the worst outcome would be if all sides dug themselves into trenches that meant no agreement was reached.

A meeting is planned for Tuesday afternoon between the culture secretary, Maria Miller, the shadow culture secretary, Harriet Harman, and the Liberal Democrat Scottish advocate general, Lord Wallace. It is the third set of cross-party talks on how to implement Leveson.

A Labour source said: “This has to be a substantive discussion, and an extended meeting. It has been nearly three weeks since Leveson was published, and so far we have made very little progress. We have put forward proposals in public. We have had nothing from the government.”

Labour also said it remained unclear what form of self-regulation the media was now proposing, partly due to the resignation of James Harding as editor of the Times.

But Labour is so exasperated by the state of the discussions that it has asked for another meeting between Miliband, Clegg and Cameron probably on Wednesday.

All three main parties are trying to find a way of appointing a government-recognised verifier tasked with ensuring a voluntary press-funded regulator does not later slip back from its agreed goal of ensuring high press standards.

Previous press commitments to reform itself have often transpired to be flawed. The group is also discussing whether statute is required to give effect to proposed incentives for the media to join the press regulator, such as lower damages settlements for privacy breaches.

Letwin has been exploring the idea of an independent group of people appointed by royal charter to verify the press regulator, so avoiding the need for statutory underpinning, something opposed by Cameron in principle and almost the entire press industry.

Labour’s negotiating hand is dependent on Clegg sticking to his previous support for statutory underpinning of the regulator. If Clegg embraces a royal charter, Miliband then faces a political choice of making the best of the agreement, or arguing it does not represent what Leveson recommended after 18 months examination of the issues.

Labour has published a draft bill establishing a verifier chaired by the lord chief justice, the head of the UK judiciary in England and Wales. The verifier would report once every three years on the performance of the regulator.

The senior Liberal Democrat peer Lord Lester has proposed a similar role be taken by president of the UK supreme court, the leader of the most senior court in the UK. The president would be required to certify that the press regulator complied with the requirements of the act before it came into force.

As a result both Labour and the Liberal Democrats have dropped Lord Leveson’s own proposal that the verifier of the press regulator be Ofcom, the current regulator for broadcasting.

Labour remains suspicious that the government is planning to produce possibly a deliberately over-complex draft bill implementing the Leveson report in a bid to show it is unworkable, and that the only practical alternative is Letwin’s royal charter.

Lord Falconer, the former Labour lord chancellor, and Labour adviser on its own draft bill, has challenged a royal charter on the basis it could be amended by the government more readily than its own proposals that require the endorsement of parliament. He has also questioned the role of the privy council in granting the regulator a charter.